In terms of the problem proposed by [1]},
the inputs and outputs consist of sequences of digits,
in which the same digit, e.g. 0 or 1,
can occur in multiple positions,
and those positions have an intrinsic order in both
the inputs and outputs.
This implies that we can meaningfully talk about moving a
digit from one position to another,
and that there is a correspondence between such motions
in the input and the output.
Convolution imposes this structure on the architecture
and makes the behaviour of the net symmetric
under these translations.
